How much current will this 16 x 2 OLED display draw when it is turned off using "noDisplay()" ?

How are these displays usually wired? Are they powered all the time even when the processor is asleep?

My project can run for a few months sleeping on a single 2400ma 3.7v battery and while I am not too concerned with the extra 30ma the OLED will draw when awake I dont want it shortening my sleep time.I have tried powering it from a digital pin ( tried powering it from 2 at once even) but this had adverse effects on some A pins I am reading.